On application of stochastic differential equations for simulation of nonlinear wave-particle resonant interactions

TL;DR

This paper investigates the use of stochastic differential equations to model nonlinear wave-particle interactions in space plasma systems, specifically focusing on energetic electron dynamics influenced by intense electrostatic waves.

Contribution

It demonstrates that nonlinear resonant effects in wave-particle interactions can be effectively modeled using stochastic differential equations with non-Gaussian energy variation distributions.

Findings

Nonlinear effects like phase trapping are captured by stochastic models.

Non-Gaussian distributions are necessary for accurate energy variation modeling.

Stochastic equations can incorporate complex wave-particle interaction effects.

Abstract

Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and electron adiabatic heating/transport by mesoscale plasma flows. Examples of such systems are Earth's radiation belts and Earth's bow shock, where ion-scale plasma injections and cross-shock electric fields determine the general electron energization, whereas electron scattering by waves relax anisotropy of electron distributions and produces small populations of high-energy electrons. The applicability of stochastic differential equations is a promising approach for including effects of resonant wave-particle interaction into codes of electron tracing in global models. This study is devoted to test of such equations for systems with nondiffusive wave-particle interactions, i.e. systems with nonlinear effects of phase trapping and bunching. We consider electron resonances with intense electrostatic whistler-mode waves often observed in the Earth's radiation belts. We demonstrate that nonlinear resonant effects can be described by stochastic differential equations with the non-Gaussian probability distribution of random variations of electron energies.